An analysis of the stationary operation of atomic clocks

TL;DR

This paper models atomic clocks to analyze their long-term stability, deriving fundamental bounds based on oscillator noise and quantum Fisher information, advancing understanding of clock synchronization dynamics.

Contribution

It introduces a comprehensive abstract model of atomic clocks, proving the existence of stationary states and deriving bounds on stability related to quantum Fisher information.

Findings

Existence of stationary states in atomic clock models

Derived fundamental bounds on long-term stability

Showed optimal variance scaling with quantum Fisher information

Abstract

We develop an abstract model of atomic clocks that fully describes the dynamics of repeated synchronization between a classical oscillator and a quantum reference. We prove existence of a stationary state of the model and study its dependence on the control scheme, the interrogation time and the stability of the oscillator. For unbiased atomic clocks, we derive a fundamental bound on atomic clocks long time stability for a given local oscillator noise. In particular, we show that for a local oscillator noise with integrated frequency variance scaling as $T^\alpha$ for short times $T$, the optimal clock time variance scales as $F^{-(\alpha +1)/(\alpha +2)}$ with respect to the quantum Fisher information, $F$, associated to the quantum reference.